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Sparse Set Membership identification of nonlinear functions and application to control of power kites for wind energy conversion

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3 Author(s)
Novara, C. ; Dip. di Autom. e Inf., Politec. di Torino, Torino, Italy ; Fagiano, L. ; Milanese, M.

A sparse approximation of a function is an approximation given by a linear combination of “many” basis functions, where the vector of linear combination coefficients is sparse, i.e. it has only “a few” non-zero elements. Identifying a sparse approximation of an unkown function from a set of data can be useful for many applications in the automatic control field: system identification, basis function selection, regressor selection, nonlinear internal model control, nonlinear feed-forward control, direct inverse control, predictive control, fast online applications. In this paper, a combined ℓ1-relaxed-greedy algorithm for sparse identification is proposed and a Set Membership optimality analysis is carried out. Assuming that the noise affecting the data is bounded in norm and that the unknown function satisfies a mild regularity condition, it is shown that the algorithm provides an almost-optimal (in a worst-case sense) approximation of the unknown function. A simulation example is shown, related to direct-inverse control of a power kite used for high altitude wind energy conversion.

Published in:

Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on

Date of Conference:

12-15 Dec. 2011